To have a chip on one's shoulder is usually an expression to describe a person who acts, as you say, rudely or aggressively, but also in a manner that could be described as "aggressively defensive." The person seems always ready for a fight.

When O.J. Simpson made the remark that he wanted to "knock that chip off Marcia Clark's shoulder," it was especially distasteful. "To knock the chip off of someone's shoulder" indicates that the speaker is ready to do battle with the person whose shoulder he is referring to. In the case of O.J. Simpson, his known history of violence made this reference all too graphic. An idiom.

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